In a small bowl, combine shallot, vinegar, and ½ teaspoon salt. Let sit, stirring occasionally, until ready to use.
In a mortar and pestle, gently crush fennel seeds and ½ teaspoon salt until seeds start to break and are fragrant.
In a large bowl, whisk oil, lemon zest and juice, and fennel salt. Add fennel, apple, radishes, and pickled shallots (discard vinegar) and toss to combine; season with salt. Top with walnuts and pomegranate seeds.
